Question

A sample of 150 is drawn from a population with a proportion equal to 0.40.Determine the probability of observing between 52 and 72successes

Answer 1

We have here given, p = 0.40 , n = 150

np = 150 * 0.40 = 60 > 10  

n(1-p) = 150 * (1-0.40) = 90 > 10

We can use here normal approximation to binomial.

P[52 < X < 72]

=P[51.5<X<72.5].........................using continuity correction.

=P[-1.42<Z<2.08]

=0.9812-0.0778...................by using normal probability table.

=0.9034